We study the stability of non-compact gradient K¨ahler–Ricci solitons under the Kähler–Ricci flow. Our main result is that appropriate perturbations of Cao’s steady soliton metric on Cn will converge to the original soliton under the Kähler–Ricci flow as time tends to infinity. These perturbations correspond to appropriately decaying perturbations of the soliton potential function; in particular, this includes any compactly supported perturbation. To obtain this result, we construct appropriate barriers and introduce an Lp-norm that decays for these barriers with non-negative Ricci curvature.

Chau, AlbertSchnürer, Oliver C.We study the stability of non-compact gradient K¨ahler–Ricci solitons under the Kähler–Ricci flow. Our main result is that appropriate perturbations of Cao’s steady soliton metric on C<sup>n</sup> will converge to the original soliton under the Kähler–Ricci flow as time tends to infinity. These perturbations correspond to appropriately decaying perturbations of the soliton potential function; in particular, this includes any compactly supported perturbation. To obtain this result, we construct appropriate barriers and introduce an Lp-norm that decays for these barriers with non-negative Ricci curvature.Chau, Alberteng2018-01-25T08:06:04ZStability of gradient Kähler-Ricci solitons2005Schnürer, Oliver C.2018-01-25T08:06:04Z